The definition of asymptotical simplicity only postulates the
existence of null infinity, \({I}\) . However, the conformal
compactification of the Minkowski spacetime in, say, the Einstein
cylinder (see e.g. [1]}, Section 6.2) shows that the conformal boundary of this spacetime contains a further point,
spatial infinity \(i^0\) , corresponding to the endpoints of
spacelike geodesics. While \({I}\)  is central in the discussion
of radiation properties of isolated bodies in General Relativity,
\(i^0\)  is key in the discussion of conserved quantities —see
e.g. [2]}, [3]}. Also, as evidenced by the stability theorems of
the Minkowski spacetime, the properties of the gravitational field in
a neighbourhood of spatial infinity is closely related to the regularity of null infinity.
